000			06066nam a22003498i 4500
001			CR9780511619700
003			UkCbUP
005			20200124160250.0
006			m|||||o||d||||||||
007			cr||||||||||||
008			090915s2007||||enk o ||1 0|eng|d
020			_a9780511619700 (ebook)
020			_z9780521883405 (hardback)
020			_z9780521709798 (paperback)
040			_aUkCbUP _beng _erda _cUkCbUP
050	0	0	_aQA403.5 _b.K36 2007
082	0	0	_a515/.2433 _222
100	1		_aKammler, David W., _d1940- _eauthor.
245	1	2	_aA first course in fourier analysis / _cDavid W. Kammler.
250			_aSecond edition.
264		1	_aCambridge : _bCambridge University Press, _c2007.
300			_a1 online resource (1 volume (various pagings)) : _bdigital, PDF file(s).
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
500			_aTitle from publisher's bibliographic system (viewed on 05 Oct 2015).
505	0		_apart 1. The mathematical core. Chapter 1. Fourier's representation for functions on R, Tp, Z, and PN. 1.1. Synthesis and analysis equations ; 1.2. Examples of Fourier's representation ; 1.3. The Parseval identities and related results ; 1.4. The Fourier-Poisson cube ; 1.5. The validity of Fourier's representation ; Chapter 2. Convolution of functions on R, Tp, Z, and PN. 2.1. Formal definitions of f * g, F x g ; 2.2. Computation of f * g ; 2.3. Mathematical properties of the convolution product ; 2.4. Examples of convolution and correlation ; Further reading ; Exercises ; Chapter 3. The calculus for finding Fourier transformations of functions on R. 3.1. Using the definition to find Fourier transformations ; 3.2. Rules for finding Fourier transformations ; 3.3. Selected applications of the Fourier transform calculus ; Further reading ; Exercises ; Chapter 4. The calculus for finding Fourier transforms of functions of Tp, Z, and PN. 4.1. Fourier series ; 4.2. Selected applications of Fourier series ; 4.3. Discrete Fourier transformations ; 4.4. Selected applications of the DFT calculus ; Further reading ; Exercises ; Chapter 5. Operator identities associated with Fourier analysis ; 5.1. the concept of an operator identity ; 5.2. Operators generated by powers of F ; 5.3. Operators related to complex conjugation ; 5.4. Fourier transforms of operators ; 5.5. Rules for Hartley transforms ; 5.6. Hilbert transforms ; Further reading ; Exercises ; Chapter 6. The fact Fourier transform. 6.1. Pre-FFT computation of the DFT ; 6.2. Deprivation of the FFT via DFT rules ; 6.3. The bit reversal permutation ; 6.4. Sparse matric factorization of F when N = 2m ; 6.5. Sparse matric factorization of H when N = 2m ; 6.6. Sparse matric factorization of F when N = P1P2...Pm ; 6.7. Kronecker product factorization of F ; Further reading ; Exercises ; Chapter 7. Generalized functions on R. 7.1. The concept of a generalized function ; 7.2. Common generalized functions ; 7.3. Manipulation of generalized functions ; 7.4. Derivatives and simple differential equations ; 7.5. The Fourier transform calculus for generalized functions ; 7.6. Limits of generalized functions ; 7.7. Periodic generalized functions ; 7.8. Alternative definitions for generalized functions ; Further reading ; Exercises -- Part 2. Selected applications. Chapter 8. Sampling. 8.1. Sampling and interpolation ; 8.2. Reconstruction of f from its samples ; 8.3. Reconstruction of f from samples of a1 * f, a2 * f, ... ; 8.4. Approximation of almost bandlimited functions ; Further reading ; Exercises ; Chapter 9. Partial differential equations. 9.1. Introduction ; 9.2. The wave equation ; 9.3. The diffusion equation ; 9.4. The diffraction equation ; 9.5. Fast computation of frames for movies ; Further reading ; Exercises ; Chapter 10. Wavelets. 10.1. The Haar wavelets ; 10.2. Support-limited wavelets ; 10.3. Analysis and synthesis with Daubechies wavelets ; 10.4. Filter banks ; Further reading ; Exercises ; Chapter 11. Musical tones. 11.1. Basic concepts ; 11.2. Spectrograms ; 11.3. Additive synthesis of tones ; 11.4. FM synthesis of tones ; 11.5. Synthesis of tones from noise ; 11.6. Music with mathematical structure ; Further reading ; Exercises ; Chapter 12. Probability. 12.1. Probability density functions of R ; 12.2. Some mathematical tools ; 12.3. The characteristic function ; 12.4. Random variables ; 12.5. The central limit theorem ; Further reading ; Exercises -- Appendices. Appendix 1. The impact of Fourier analysis ; Appendix 2. Functions and their Fourier transforms ; Appendix 3. The Fourier transform calculus ; Appendix 4. Operators and their Fourier transforms ; Appendix 5. The Whittaker-Robinson flow chart for harmonic analysis ; Appendix 6. FORTRAN code for a randix 2 FFT ; Appendix 7. The standard normal probability distribution ; Appendix 8. Frequencies of the piano keyboard.
520			_aThis book provides a meaningful resource for applied mathematics through Fourier analysis. It develops a unified theory of discrete and continuous (univariate) Fourier analysis, the fast Fourier transform, and a powerful elementary theory of generalized functions and shows how these mathematical ideas can be used to study sampling theory, PDEs, probability, diffraction, musical tones, and wavelets. The book contains an unusually complete presentation of the Fourier transform calculus. It uses concepts from calculus to present an elementary theory of generalized functions. FT calculus and generalized functions are then used to study the wave equation, diffusion equation, and diffraction equation. Real-world applications of Fourier analysis are described in the chapter on musical tones. A valuable reference on Fourier analysis for a variety of students and scientific professionals, including mathematicians, physicists, chemists, geologists, electrical engineers, mechanical engineers, and others.
650		0	_aFourier analysis.
776	0	8	_iPrint version: _z9780521883405
856	4	0	_uhttps://doi.org/10.1017/CBO9780511619700
999			_c519410 _d519408